Interferometric distance measurement based on compression of chirped interferogram from cross-chirped interference

ABSTRACT

Disclosed herein are interferometric measurement systems and methods. In one exemplary embodiment an interferometric measuring system for measuring the distance to or displacement of an object includes: a light source; an interferometer with a measuring arm and a reference arm; a dispersive medium; and a detector. The interferometer is disposed between the light source and the object. The dispersive medium is arranged to unbalance the dispersion between the measurement arm and the reference arm. The detector is arranged to detect spectrum interference from the interferometer. In one example, the dispersive medium is a chirped fiber Bragg grating. In another example, the dispersive medium is a highly dispersive optical fiber. In one example, the light source is a broadband light source, and the detector includes a spectrometer. In another example, the light source is a wavelength swept laser, and the detector includes a photodetector or a balanced photodetector.

RELATED APPLICATION

This application claims priority to U.S. Provisional Patent ApplicationSer. No. 62/252,065, titled “Interferometric Distance Measurement Systemand Method Based on Compression of Chirped Interferogram fromCross-chirped Interference,” which was filed on Nov. 6, 2015, which isexpressly incorporated by reference herein in its entirety.

FIELD OF INVENTION

The present disclosure generally relates to systems and methods formeasuring distance and displacement. More specifically, the presentdisclosure relates to novel interferometric systems and methods formeasuring distance and displacement using compression of a chirpedinterferogram generated from cross-chirped interference.

BACKGROUND

In a variety of commercial, industrial, and academic endeavors theaccurate and precise measurement of distances is vital to accomplishingcritical tasks. One metrology technique that is widely used is opticalinterferometry. Optical interferometric devices can be used to measurethe distance to an object or surface or to measure the displacement ofthat object or surface over time. Such optical interferometric devicescan be integrated into objects with large scale volumes to measurecoordinates within that volume, particularly where a cooperative target(i.e., a target that reflect light back to a detector) is present. Whenno cooperative target is available, optical interferometric devices canscan a target or surface to gather information about the target orsurface.

With the cooperative target, a wavelength-stabilized laserinterferometer, commonly referred to as a “laser tracker,” has been usedfor displacement measurements. Commercially available laser trackers candetermine displacement by continuously counting incrementaldisplacement, which can be determined from counting longitudinalinterference fringes. Since the fringe needs to be continuously counted,the laser beam from the laser tracker must be subject to a beam trackingmethod that does not break the beam from the cooperative target. Such anarrangement is possible when the cooperative target is a corner cuberetroreflective target with a spherical back surface for which the innercenter is aligned with the center of the reflector. Such a corner cubeis commonly referred to as a spherically mounted retroreflector (“SMR”).The resolution of displacement measurements are a few folds ofwavelength. An optical interferometer with a stabilized helium-neonlaser could provide the resolution of half the wavelength (λ/2=316.5nm). The accuracy of the measurement depends upon the stability of thewavelength and the sensitivity of the sensors, i.e., how the accuracy ofthe sensor is affected by environmental factors, such as temperature,pressure, and humidity. Thus, the accuracy of distances measured withoptical interferometer is reliable so long as the wavelength of light isstable and traceable with a reference light source.

While the described SMR tracking interferometer with awavelength-stabilized laser that is arranged to account forenvironmental conditions can provide relatively high resolution andhigh-speed distance measurements, to measure the absolute distance to anon-cooperative target or scan along a surface of a three-dimensionalobject, typically requires a broadband or wavelength-tunable lightsource. Frequency modulated coherent laser radar (“FM-LR”) is onebroadband interferometry technique that uses a wavelength-tunable lightsource. FIG. 1 schematically illustrates an exemplary FM-LR 10 known inthe prior art.

FM-LR is generally analogous to conventional radar techniques, but isapplied to the optical domain using coherence of light. In a radarsystem, a sweep of a radio frequency (“RF”) wave is mixed with a localoscillator, which serves as a reference for the sweep. The beatingfrequency, defined by the frequency difference between the receivingsignal and the local oscillator, provides the inverse of thetime-of-flight of the receiving RF wave, which can be translatedlinearly into distance. In FM-LR, the optical frequency is swept in timefor the sweep, where the local oscillator is created by splitting theswept source beam. The light from the measurement arm in theinterferometer is combined with the local oscillator from the referencearm. If the optical path lengths from both the measurement arm and thereference arm are within the coherence length of the light source,interference will be realized in the wavelength sweep, which isproportional to the inverse of the swept wavelength linewidth.

In an example of a basic implementation, the Fourier transformation ofthe acquired interferogram, calibrated in optical frequency coordinate,will provide a point spread function (“PSF”) of the light reflected froma target surface. For the PSF, distance information can be determined bydetermining the peak of the PSF. The precision of the distancedetermination relies on the algorithm used along with thesignal-to-noise ratio (“SNR”). In general, with an SNR of 0 dB (i.e.,the noise amplitude is the same as the signal amplitude), the distancerepeatability in terms of the standard deviation is typically about 50folds of the full width at half maximum (“FWHM”) of the PSF.

When FM-LR is applied to non-contact volumetric metrology, typically afast tunable light source is used. The frequency of the light source canbe either externally modulated with an acousto-optic tunable filter ordirectly modulated by a driving current modulation. The frequencymodulation bandwidth can be as high or higher than 50 GHz depending uponthe frequency swept speed. The bandwidth is inversely proportional tothe width of the PSF. For example, the 50 GHz band for a rectangularfrequency sweep corresponds to the FWHM of the PSF of 4 mm. For directcurrent modulation, the linewidth, defined by the FWHM of a Gaussianspectral density of a distributed feedback laser diode could be asnarrow as 5 MHz, which can be translated into a vacuum-space coherencelength of 26.4 meters. At 0 dB SNR, the repeatability in standarddeviation can be about 0.04 mm.

The FM-LR technique is useful because of its inherent background ambientlight rejection, high sensitivity, and high resolution in a very longdistance measurement range. However, due to the wave length tuningmechanism, the tuning speed needs to be significantly low in order tofacilitate scanning of a three-dimensional surface of an object. Forexample, it may be possible to obtain sweep frequency up to 5 kHz with50 GHz sweep bandwidth, but it would be difficult to obtain higherwithout compromising the resolution.

Another broadband interferometry technique known in the art is spectraldomain reflectometry. FIG. 2 schematically illustrates a system 20 forfacilitating a spectral domain reflectometry technique. The spectraldomain reflectometry technique is based on the measurement of theinterference pattern between light that is emitted from a broadbandsource 22 and split between a measurement arm 24 and a reference arm 26of the interferometer. As is illustrated in FIG. 2, a portion of thelight emitted from the broadband source 22 is transmitted through themeasurement arm 24 of the interferometer to a target 28 to becharacterized, where the light is reflected off the target 28 and backthrough the measurement arm 24. Another portion of the light emittedfrom the broadband source 22 is transmitted through the reference arm 26of the interferometer to a mirror 30, where it is reflected back throughthe reference arm 26. The light reflected back through the reference arm26 is a coherent reference light, i.e., a local oscillator. The lightreturned from the measurement arm 24 and a reference arm 26 of theinterferometer is combined and interference is measured in the frequencyor wavelength domain. In order to acquire the spectral interference,which corresponds to the beating frequency information between the lightreturned from the measurement arm 24 and a reference arm 26 of theinterferometer (the local oscillator), the method acquires the spectrumdirectly in the spectral domain instead of sweeping a narrow linewavelength laser. High resolution spectrometer is used for acquiring thespectrogram. A high speed line scan camera can be used for high speedmeasurement. The measured spectral domain information is converted intothe desired length domain information by use of discrete Fouriertransformation, which is calculated with signal processors 32.

Currently, affordable line-scan cameras can ramp the measurement speedup to 100,000 lines per second. Since the source does not need to beswept in optical frequency, a broadband light source, such as a lightemitting diode or a super luminescent laser diode, can be used. Thedistance range is limited by the spectrometer resolution. For example, ahigh resolution of 0.06 nm at 850 nm corresponds to the coherent lengthof 5.3 mm in a vacuum. With a light source with 40 nm FWHM Gaussianspectrum, one can achieve 8 μm FWHM of the PSF. Because the PSF isnarrow enough to determine nano-scale features, this technique is used,for example, in semiconductor parts inspection. However, due to thespectral resolution limit, this technique is not feasible for highprecision volumetric measurement in metrology for industrialapplications.

The aforementioned interferometers and techniques for metrology havelimitations. For the prior art interferometers and techniques, rangedetection limits the measurement ranges based on the coherence length ofthe interferometer system. Such interferometers and techniques can covereither a very long range with low speed (5,000 measurements per second)and moderate repeatability (0.04 mm) for scanning, or a very short range(5.3 mm) with high speed (80 kHz) and high repeatability (80 nm), butnot both. These interferometers and techniques are not suitable forcovering mid-range (from about 0.1 meter to a few meters) with highspeed (i.e., greater than 50,000 measurements per second) andrepeatability better than 0.001 mm.

In the U.S. Pat. No. 8,094,292, titled “Cross-chirped InterferometrySystem and Method for Light Detection and Ranging,” issued to aco-Applicant, the disclosure of which is incorporated herein byreference, an interferometric system and method are described forobtaining high-speed, high-precision and high-sensitivity time-of-flightoptical range finding or position identification, which allows a directtime-of-flight to spectrum mapping to achieve spectral domainacquisition for the time-of-flight detection.

SUMMARY

Disclosed herein are interferometric measurement systems and methods. Inone exemplary embodiment an interferometric measuring system formeasuring the distance to or displacement of an object includes: a lightsource; an interferometer with a measuring arm and a reference arm; adispersive medium; and a detector. The interferometer is disposedbetween the light source and the object. The dispersive medium isarranged to unbalance the dispersion between the measurement arm and thereference arm. The detector is arranged to detect spectral interferencefrom the interferometer. In one example, the dispersive medium is achirped fiber Bragg grating. In another example, the dispersive mediumis a highly dispersive optical fiber. In one example, the light sourceis a broadband light source, and the detector includes a spectrometer.In another example, the light source is a wavelength swept laser, andthe detector includes a photodetector or a balanced photodetector.

An exemplary method of reconstructing a point spread functionnumerically from an acquired localized symmetric balanced interferogramfrom the interferometer includes the steps of: providing aninterferometer disposed between a light source and an object, and havinga reference arm and a measurement arm; applying background subtractionto balance the amplitude of the interferogram; applying a high passfilter to suppress residual background spectrum; applying a Fourierdomain filter in the Fourier domain to compress the chirpedinterferogram numerically; applying an inverse Fourier transform todetermine the absolute value to construct the point spread function; andapplying a peak detection algorithm to search the matched wavelengthwith the point spread function.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings, structures are illustrated that, togetherwith the detailed description provided below, describe exampleembodiments of the disclosed systems, methods, and apparatus. Whereappropriate, like elements are identified with the same or similarreference numerals. Elements shown as a single component can be replacedwith multiple components. Elements shown as multiple components can bereplaced with a single component. The drawings may not be to scale. Theproportion of certain elements may be exaggerated for the purpose ofillustration.

FIG. 1 schematically illustrates a frequency modulated coherent laserradar known in the art.

FIG. 2 schematically illustrates a spectral domain reflectometry knownin the art.

FIG. 3 schematically illustrates a cross-chirp interference (XCI)interference system according to an embodiment of this disclosure.

FIG. 4 schematically illustrates a system configuration using aspectrometer as an embodiment of this disclosure.

FIG. 5 schematically illustrates a system configuration using awavelength swept laser as an embodiment of this disclosure.

FIG. 6 illustrates a numerical example of a cross-chirped spectralinterferogram which can be acquired from the interferometer and thepoint spread function after numerical processing.

FIG. 7 illustrates a flow chart for implementing methods describedherein.

FIG. 8 illustrates a functional block diagram of signal processing asdescribed herein.

DETAILED DESCRIPTION

The apparatus, systems, arrangements, and methods disclosed in thisdocument are described in detail by way of examples and with referenceto the figures. It will be appreciated that modifications to disclosedand described examples, arrangements, configurations, components,elements, apparatus, methods, materials, etc. can be made and may bedesired for a specific application. In this disclosure, anyidentification of specific techniques, arrangements, method, etc. areeither related to a specific example presented or are merely a generaldescription of such a technique, arrangement, method, etc.Identifications of specific details or examples are not intended to beand should not be construed as mandatory or limiting unless specificallydesignated as such. Selected examples of apparatus, arrangements, andmethods for measuring distance and displacement using compression of achirped interferogram generated from cross-chirped interference arehereinafter disclosed and described in detail with reference made toFIGS. 1-8.

The systems and methods disclosed herein are directed to allowing themeasurement of distance and/or displacement of a target or object beyondthe coherent length of a light source, with signal processing to enhancedetection sensitivity and distance measurement repeatability. Thesystems and methods disclosed herein are generally based on a dispersionunbalanced interferometer, which enables projections of light echoesfrom an object or target to an optical spectrum. From the opticalspectrum, spectrally-encoded coherent time-of-flight can be detectedwith high precision. The systems and methods described herein, can beapplicable, for example, for absolute distance ranging, laserthree-dimensional scanning, laser radar, biomedical imaging for surgicalguidance.

Disclosed herein are enhancements to cross-chirped interferometer,achieved by applying a novel numerical algorithm, a new processingschematic, and a new system configuration based on the system describedin co-Applicant's above-noted earlier patent. The absoluteinterferometric technique and processing algorithm disclosed hereinprovide a laser system enabling cost effective system integration andhigh precision, high-speed measurement for three-dimensional objectscanning.

In an exemplary embodiment, a system includes a Michelsoninterferometer, with a measurement arm and a reference arm, a broadbandlight source, and a spectrometer for acquiring spectral interferogram. Alinearly chirped fiber Bragg grating is used in the interferometerreference arm so that the broadband light is reflected from the gratingwith a large dispersion, whereas in the measurement arm, light isreflected from a target surface without the large dispersion. Theinterference is made in the spectrometer in which the acquiredspectrogram contains a localized chirped interferogram. The spectralcenter of the chirped interferogram along the wavelength indicates thephysical location of the grating fringe where the particular wavelengthof light reflected back interferes with the corresponding optical pathlength of light reflected back from the target surface. The depth of thetarget can be measured by determining the spectral center of the chirpedinterferogram.

In the co-Applicant's above-noted patent, two approaches were used fordetermining the spectral center. One is to extract the envelope of thechirped waveform by dithering one of the interferometer arm with a phasemodulator. This approach is not suitable for high speed measurements.The other method is to collect two different interferograms with90-degree phase shift which requires a sophisticated optical system andalignment.

In the embodiments disclosed herein, a single interferogram is acquiredwithout using a phase modulation or an interferogram with 90-degreephase shift. Instead, the Fourier transform of the interferogram isfiltered numerically by a Fourier-domain filter to compress the chirpedinterferogram to a transform-limited point spread function. TheFourier-domain filter can be prepared in a number of different ways. Oneexample is to create a numerical interferogram based on the dispersionof the grating and the wavelength of the broadband source and to takeits Fourier transform. This allows the use of a simple interferometerconfiguration as described above at high acquisition speed. Moreover,since the chirped interferogram is compressed, the signal detectionsensitivity is greatly improved compared to the previous detectionmethod.

A practical system can be configured as disclosed herein withmeasurement range from a millimeter to a few meters and repeatabilityfrom few nanometers to a few microns at high speed limited by eitherline-scan camera acquisition (e.g. greater than 80,000 lines per sec) orwavelength swept speed (e.g. greater than 200,000 sweep per sec).

Cross-chirp interference (XCI) is an interferometric technique tomeasure absolute distance using a linearly chirped fiber Bragg gratingas a linear distance reference. Any high dispersion medium with matcheddelay can be used as a replacement from the grating. Such highdispersion medium includes a spool of optical fiber and diffractiongrating pairs.

A known system 100 disclosed in the above-noted co-Applicant patent isschematically illustrated in FIG. 3. The system 100 includes awavelength swept laser source 110 that emits light 120, a measurementarm 130, and a reference arm 140. The wavelength swept laser source 110emits continuous sweeps of optical wavelength in time with a finitespectral linewidth. The light 120 from wavelength swept laser source 110is split between the measurement arm 130 and reference arm 140. A fiberoptic circulator 150 is integrated into the reference arm 140. Theportion of light in the reference arm 140 is routed to a dispersionmedium via the fiber optic circulator 150. In the system 100 of FIG. 3,the dispersion medium is a fiber Bragg grating 160 with large groupdelay dispersion, {umlaut over (Φ)}₀. The light 120 in the reference arm140 is reflected at a local fringe of the grating, where the incidentwavelength matches with the Bragg wavelength. If the fiber Bragg grating160 is linearly chirped, the swept wavelengths will be reflected alongthe grating with linear depth of reflection. A fiber optic circular 170is integrated into the measurement arm 120. The portion of light in themeasurement arm 130 is routed to a beam focusing optic 180 via the fiberoptic circulator 170. The light is then reflected by the target 190.

The depth of the reflection (L) with spectrum bandwidth (Δλ) can bedefined with the following equation:

c·Δλ·{umlaut over (Φ)} _(λ)/2=L

where {umlaut over (Φ)}_(λ)=2πc{umlaut over (Φ)}₀/λ₀ ²

-   -   c is speed of light    -   λ₀ is wavelength of the light source

In contrast to the dispersive light reflection through the reference arm140, the light from the measurement arm 130 is reflected from the target190 without spectral depth of reflection. If the depth of reflection inthe measurement arm 130 matches with the spectral depth of reflection ata certain wavelength in the reference arm 140, interference occurs nearthe wavelength when the two beams are combined. The system includes abalanced receiver 200 to detect the interference. The balanced receivercan be a photodetector or a balanced photodetector. More specifically,the interference appears broadly around the matching wavelength as asymmetrically chirped waveform, i.e., the interference is visible notonly on the delay matched wavelength but also on the wavelengths aroundthe delay matched wavelength. This is due to the interference beingdetectable as long as the optical path length difference is comparableto the coherence length of the wavelength swept laser line. Since thematching wavelength indicates the depth of reflection, the distancemeasurement can be determined from the matching wavelength. Thelocalized chirped interference moves along the wavelength as the depthof reflection from the target 190 changes, meaning that the spectralmodulation frequency by the interference and its bandwidth remain thesame except for the matching wavelength shift. Whereas for FM-LR, themodulation frequency increases as the depth of reflection increases andthe depth is limited by the coherence length. This is the reason why themeasurement range of the present XCI invention can exceed the coherencelength of the light source.

One of the methods to determine the matching wavelength in theco-Applicant's above-noted patent is to extract the envelope of thechirped interferogram by modulating the phase of the reflected lightwith a frequency much higher than the wavelength sweep frequency. As inthe system 100 in FIG. 3, a fiber optic phase modulator 210 can be usedwith the system 100. The envelope profile can be extracted by mixing thelocal oscillations. The detection sampling rate has to be at least twiceas high as the modulation frequency, which is a high sampling rate. Inanother embodiment, a 90-degree shifted coherent photo receiver can beused with the system 100. The 90-degree shifted coherent photo receiveracquires two balanced interferences, where the modulation phase is90-degrees shifted relative to each other. This permits the envelopeprofile to be extracted without the use of the phase modulator 210.

Advantages of the systems and methods disclosed herein are improvementsof the distance measurement repeatability and simplification of thedetection of the interferogram for obtaining the point spread function.

An exemplary system 300 is schematically illustrated in FIG. 4. Thesystem 300 includes a broadband light source 310 that emits light 320and a Michelson fiber optic interferometer with a measurement arm 330and a reference arm 340. The broadband light source 310 can be a superluminescent diode. The broadband light source 310 emits continuous lightthrough a fiber coupler 350. The fiber coupler 350 splits the power ofthe light and directs a first portion to a fiber Bragg grating 360 inthe reference arm 340 and directs a second portion to beam focusingoptics 370 in the measurement arm 330 and on to a target 380. Reflectedlight from the grating 360 is combined with the light reflected from thetarget 380 via the fiber optic coupler 350 and the interference iscaptured in the spectrometer 390. Although the system 300 of FIG. 4illustrates a spectrometer in use with a broadband light source, if thelight source is a wavelength swept laser, a single photodetector can beused by that system.

Another exemplary system 400 is schematically illustrated in FIG. 5. Thesystem 400 uses a balanced detector 410 together with the wavelengthswept laser 420. In this system 400, there is no phase modulation ordemodulation algorithm used. This becomes a conventional wavelengthswept coherent reflectometry with the addition of the chirped fiberBragg grating 430.

For the methods disclosed herein, there is no need to attempt tomodulate or acquire additional interferograms. A numerical correlationof the chirped interferogram is performed knowing what waveform isexpected to be acquired from the detector, except for the matchingwavelength center. The waveform is deterministic since the chirpedinterferogram can be simulated based on the wavelength of the source andthe dispersion of the chirped fiber Bragg grating. The correlationcalculation can be implemented in the Fourier domain by multiplying theFourier transform of the simulated interferogram, yielding a highdefinition, transform-limited point spread function.

FIG. 6 depicts two graphs. The upper graph shows the simulated waveformconstructed with a Gaussian spectrum centered at 850 nm, with 30 nmFWHM, 0.06 nm spectral resolution and with the group delay dispersion of10 ps-per-nanometer (ps/nm), and the background spectrum subtracted. Thelower graph shows the self-correlation of the waveform obtained byperforming the correlation in the Fourier domain, where the FWHM of thePSF is 0.14 mm. Considering that the FWHM of the interference envelopeis 1.2 nm, corresponding to 1.8 mm in depth, the compression ratio (theFWHM PSF divided by FWHM envelope) is 0.07. To make this compressioneffective, i.e., a smaller ratio, requires a smaller spectralresolution, meaning that the optical frequency resolution should be muchsmaller. For example, if the spectral resolution is reduced in half,i.e. 0.03 nm, the FWHM PSF becomes 0.067 mm, whereas the FWHM envelopeincreases to 3.3 mm, resulting in a compression ratio of 0.02.

The signal processing of the chirped interferogram is illustrated in theflow diagram 500 of FIG. 7. In a first step, a spectrum with alocalized, symmetrically-chirped interferogram is acquired (step 510) bya photodetector, a spectrometer, or other apparatus. In the next step, apre-acquired source spectrum is used to subtracted the backgroundspectrum on the acquired interferogram (step 520). The background can beobtained by pre-acquiring the spectrum from the reference arm when themeasurement arm is blocked and another spectrum from the measurement armwhen the reference arm is blocked. The first spectrum is constantregardless of target measurement condition. The second spectrum isvariable depending upon the return power from the measurement arm. Thereturn power measurement can provide the scale of the spectrum. Anumerical, high-pass filtering may be applied in addition to thebackground subtraction to remove residual background. A numericalexample of an interferogram after the background subtraction is shown inFIG. 6. The interferogram becomes a localized, symmetrically-chirpedbalanced waveform with respect to optical frequency. For a calibratedspectrameter, the waveform can be directly acquired with respect to anequally-spaced wavelength that can be further interpolated into anequally paced optical frequency for converting into depth of reflection(i.e., distance). For a wavelength swept laser, a sampling clock may beused to linearize the waveform with respect to the optical frequency (orwavenumber). The depth of reflection can be calculated for the gratinglinearly chirped with respect to optical frequency, for example by thefollowing equation:

$2{{\pi \left( {f - f_{s}} \right)} \cdot {\overset{¨}{\Phi}}_{0}}\frac{c}{2}$

where f_(s) is the wavelength having the shortest depth of reflection.

The Fourier transform (step 530) of the waveform is multiplied by agiven complex filter (step 540), which can be obtained numerically orempirically. An interferogram may be acquired directly from theinterferometer with a reflective target at the center of the depth ofreflection, and the spectral background subtracted from it. The complexfilter in the Fourier domain (step 540) is obtained by taking a discreteFourier transform of the balanced interferogram with respect to thewavelength. This can be used as the Fourier domain filter for thewaveform compression empirically. Another way is to create thesymmetrically-chirped waveform numerically, using the followingequation:

exp(−f ²/(2df ²))·cos(2π²{umlaut over (Φ)}₀ f ²)

where: f is the base frequency defined by (optical frequency−centerfrequency); and

-   -   df is the interference waveform width.

A similar waveform can be found in a radar technology, the so called“synthetic aperture radar.” However, it is used in radar radiation,artificially created/modulated incoherent wave, for determining therange. For the systems and methods disclosed herein, it is applied tonatural coherent waveforms created in the cross-chirp interference.

Another reference waveform may be prepared separately forphase-sensitive PSF amplitude modulation. Such a waveform has its phaseshifted by 90 degrees relative to the first waveform,exp(−f²/(2df²))·sin(2π²{umlaut over (Φ)}₀f²).

Once the Fourier domain filters are multiplied to the Fouriertransformed chirped interferogram yielding two complex-filteredwaveforms, zero paddings may be applied to both waveforms (step 550),depending upon the sampling resolution prior to the inverse Fouriertransformation, to increase the sampling resolution in wavelength (realdomain). The filtering process is completed by taking absolutes of theinverse discrete Fourier transformation of the filtered Fourier waveform(step 560). The square root of the squared sum of theinversely-transformed waveforms is shown in the bottom graph of FIG. 6.When the waveform compression is effective (i.e., smaller compressionratio), the PSF amplitude is stable and does not require the secondreference waveform to be applied. However, in case the compression isless effective (i.e., higher compression ratio), the additionalprocessing with the 90-deg shifted reference waveform helps the PSFamplitude to be less modulated by the interference fringe shift.

There are many different methods to determine the peak of the PSF. Oneexample is to take the derivative of the PSF (step 570) or high-passfilter to reform it into a doublet pulse where the center of the pulseprofile crosses zero amplitude (step 580). A linear fitting may beapplied to determine zero-crossing wavelength (λ). The zero-crossingwavelength is converted into the depth of reflection. Alternatively,direct quadratic fit may be directly applied to the PSF instead of thederivative.

FIG. 8 illustrates an exemplary block diagram 600 for implementing thesystems and methods disclosed herein. As illustrated, an interferogramis acquired 610, and two numerical references are generated 620. Thebackground is removed 630 from the interferogram, and a Fouriertransform 640 is applied to the two numerical references. The output ofboth processes are passed to a numerical convolution process 650. In thenumerical convolution process 650, a Fourier transform 660 is appliedthe modified interferogram, and the result is combined 670 with the twonumerical references. The result is passed through a zero-pad and anotch filter 680 and then an inverse discrete Fourier transform 690 isapplied to yield a result 700. A peak search 710 is applied to theresult, and a wavelength to distance conversion 720 is performed, whichyields a distance output 730.

The foregoing description of examples has been presented for purposes ofillustration and description. It is not intended to be exhaustive orlimiting to the forms described. Numerous modifications are possible inlight of the above teachings. Some of those modifications have beendiscussed, and others will be understood by those skilled in the art.The examples were chosen and described in order to best illustrateprinciples of various examples as are suited to particular usescontemplated. The scope is, of course, not limited to the examples setforth herein, but can be employed in any number of applications andequivalent devices by those of ordinary skill in the art.

We claim:
 1. An interferometric measuring system for evaluating anobject, comprising: a light source; an interferometer positioned betweenthe light source and the object, the interferometer comprising ameasuring arm and a reference arm; a dispersive medium coupled to thereference arm; a detector for detecting a spectrum of interference ofthe interferometer; and a digital signal processing unit that includes across-chirp interference compression algorithm.
 2. The interferometricmeasuring system of claim 1, wherein the dispersive medium is a chirpedfiber Bragg granting without phase modulator.
 3. The interferometricmeasuring system of claim 2, wherein, the grating can be linearlychirped with respect to either wavelength or optical frequency.
 4. Theinterferometer measuring system of claim 1, wherein the light source isa broadband light source.
 5. An interferometric measuring system ofclaim 3, wherein the broadband light source is a super luminescentdiode.
 6. The interferometer measuring system of claim 1, wherein thedetector is a spectrometer.
 7. The interferometer measuring system ofclaim 1, wherein the dispersive medium that unbalances the dispersionbetween the measurement arm and the reference arm.
 8. The interferometermeasuring system of claim 1, further comprising a digital signalprocessing unit to evaluate an output from the detector.
 9. Theinterferometric measuring system of claim 1, where the light source is awavelength swept laser.
 10. The interferometric measuring system ofclaim 8, where the detector is a photodetector or a balancedphotodetector.
 11. The interferometric measuring system of claim 1,where the dispersive medium is one of dispersion compensating fiber,diffraction grating, or multimode fiber.
 12. The interferometricmeasuring system of claim 1, further comprising a fiber coupler thatsplits light between the measure arm and the reference arm.
 13. A methodfor reconstructing a point spread function from an acquired localizedsymmetrically chirped balanced interferogram from a interferometer,comprising the steps: applying a background subtraction to balance anamplitude of the interferogram; applying a high pass filter to suppressresidual background spectrum; and applying a Fourier domain filter inthe Fourier domain to compress the chirped interferogram numerically.14. The method of claim 13, wherein the Fourier domain filter isprepared numerically by knowing the spectrum of light source and thegroup delay dispersion of the dispersive medium.
 15. The method of claim13, wherein Fourier domain filter is prepared by applying a Fouriertransform to the reference interferogram.
 16. The method of claim 12,wherein the Fourier domain filter is prepared empirically by capturingthe spectral interferogram from the system using a reflective targetcentered at the depth of reflection and subtracting the background tobalance the amplitude.
 17. The method of claim 12, further comprisingthe step of: applying the inverse Fourier transform and taking theabsolute value to construct the point-spread function.
 18. The method ofclaim 12, further comprising the step of: applying a peak detectionalgorithm to search the matched wavelength with the point spreadfunction.